Electronic Journal of Probability

Asymptotics of the rising moments for the coupon collector's problem

Aristides Doumas and Vassilis Papanicolaou

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Abstract

We develop techniques of computing the asymptotics of the moments of the number $T_N$ of coupons that a collector has to buy in order to find all $N$ existing different coupons as $N\rightarrow \infty.$ The probabilities (occurring frequencies) of the coupons can be quite arbitrary. After mentioning the case where the coupon probabilities are equal we consider the general case (of unequal probabilities). For a large class of distributions (after adopting a dichotomy) we arrive at the leading behavior of the moments of $T_N$ as $N\rightarrow \infty.$ We also present various illustrative examples.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 41, 15 pp.

Dates
Accepted: 22 March 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064266

Digital Object Identifier
doi:10.1214/EJP.v18-1746

Mathematical Reviews number (MathSciNet)
MR3040551

Zentralblatt MATH identifier
1283.60035

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F99: None of the above, but in this section

Keywords
Coupon collector's problem higher asymptotics

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Doumas, Aristides; Papanicolaou, Vassilis. Asymptotics of the rising moments for the coupon collector's problem. Electron. J. Probab. 18 (2013), paper no. 41, 15 pp. doi:10.1214/EJP.v18-1746. https://projecteuclid.org/euclid.ejp/1465064266


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